Generalized Tensor Decomposition - Utility for Data Analysis

Explore the power of generalized tensor decomposition for data analysis in this 57-minute webinar. Dive into unsupervised learning methodologies applicable to chemometrics, criminology, and neuroscience. Learn about low-rank tensor decomposition using canonical polyadic or CANDECOMP/PARAFAC format, and understand the limitations of the standard sum of squares error (SSE) metric. Discover alternative objective functions like KL divergence for count data, logistic odds for binary data, and beta-divergence for nonnegative data. Examine real-world applications, including a detailed analysis of Chicago Crime Data from 2019. Explore computational aspects of generalized tensor decomposition, current research, and open challenges in the field. Follow along with topics such as matrix decomposition, CP optimization problems, probabilistic interpretations, and stochastic sampling methods. Gain insights into the utility of these techniques for complex data analysis across various domains.

Intro
Example Application: Chicago Crime Data
Chicago Crime Data (2019)
Warm-up: Matrix Decomposition
CP Optimization Problem (d-way)
Probabilistic Interpretation of Standard CP
Connection to Least-Squares Loss
Statistical Framework for Loss Function
"Poisson" CP for Count Data
Binary CP with Odds Link
GCP Optimization Problem (3-way)
2019 Chicago Crime Data - Count Data
Rank-7 Decomp
Component 7 (of Rank 7)
Revisiting GCP Optimization (3-way)
Uniform Sampling
Stratified Zero/Nonzero Sampling
Stochastic Method Performance
Summary and Open Problems